arXiv subjects

Christos A. Tsonos

Publications and source records attributed to Christos A. Tsonos.

10 recordsLinked to original sources

arXiv2026

A new class of degenerate solutions to the massless Dirac equation and their potential applications in optical memories

In this article, we present a novel class of degenerate solutions to the massless Dirac equation, corresponding to a wide variety of electromagnetic 4-potentials and fields, including both zero field and circularly polarized electromagnetic waves. An interesting property of these solutions is that the spin of the particles rotates in synchronization with the electric and magnetic fields of the electromagnetic waves. These results could be utilized for the development of optical memories based on materials supporting massless Dirac fermions, such as graphene.

quant-ph↗

arXiv2025

Localized degenerate solutions to the massless Dirac and Weyl equations

In this article we present a general class of localized degenerate solutions to the massless Dirac and Weyl equations, which can also describe particles, or systems of particles, with varying energy and spin along their direction of motion. Another interesting characteristic of these solutions is that they remain unaltered in a wide range of electromagnetic 4-potentials and fields, which are analytically calculated. In addition, we propose a new method for spatially separating Weyl particles based on their helicity and direction of motion using appropriate magnetic fields, given in explicit form.

quant-ph↗

arXiv2025

Degenerate solutions to the Dirac and Weyl equations and their applications

In this review article we present a comprehensive review of degenerate solutions to the Dirac and Weyl equations, highlighting novel and significant findings. Specifically, we demonstrate that all Weyl particles, and under certain conditions Dirac particles, can occupy the same quantum state under an extensive range of electromagnetic 4-potentials and fields. These fields, which are infinite in number, have been explicitly derived and analysed. Additionally, we establish that Weyl particles can form localized states even in the absence of external electromagnetic fields. Moreover, we show that their localization can be precisely controlled through the application of simple electric fields, offering a tuneable mechanism for manipulating these particles. Building on these insights, we propose an innovative device that utilizes Weyl fermions to control the flow of information at an unprecedented rate of up to 100 petabits per second. This finding has significant implications regarding the development of next-generation electronic and quantum information technologies, as it presents a fundamentally new approach to high-speed data processing and transmission.

quant-ph↗

arXiv2024

A novel device for controlling the flow of information based on Weyl fermions and some interesting remarks regarding the electromagnetic interactions of high energy particles

In this work we propose a novel device for controlling the flow of information using Weyl fermions. Based on a previous work of our group, we show that it is possible to fully control the flow of Weyl fermions on several different channels, by applying an electric field perpendicular to the direction of motion of the particles on each channel. In this way, we can transmit information as logical bits, depending on the existence or not of a Weyl current on each channel. We also show that the response time of this device is exceptionally low, less than 1 ps, for typical values of its parameters, allowing the control of the flow of information at extremely high rates, of the order of 100 Petabits per second. Alternatively, this device could also operate as an electric field sensor. In addition, we demonstrate that Weyl fermions can be efficiently guided through the proposed device using appropriate magnetic fields. Finally, we discuss some particularly interesting remarks regarding the electromagnetic interactions of high energy particles.

quant-ph↗

arXiv2022

A general method for obtaining degenerate solutions to the Dirac and Weyl equations and a discussion on the experimental detection of degenerate states

In this work we describe a general method for obtaining degenerate solutions to the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. In more detail, using four arbitrary real functions, one can automatically construct a spinor which is solution to the Dirac equation for an infinite number of electromagnetic 4-potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with non-zero mass, the degenerate spinors should be localized, both in space and time. Our method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, we propose two experimental methods for detecting the presence of degenerate states.

quant-ph↗

arXiv2022

Degenerate wave-like solutions to the Dirac equation for massive particles

In this work we provide a novel class of degenerate solutions to the Dirac equation for massive particles, where the rotation of the spin of the particles is synchronized with the rotation of the magnetic field of the wave-like electromagnetic fields corresponding to these solutions. We show that the state of the particles does not depend on the intensity of the electromagnetic fields but only on their frequency, which is proportional to the mass of the particles and lies in the region of Gamma/X-rays for typical elementary charged particles, such as electrons and protons. These novel theoretical results could play an important role in plasma physics, astrophysics, and other fields of physics, involving the interaction of charged particles with high energy photons.

quant-ph↗

arXiv2022

On the remarkable properties of Weyl particles

In this work we show that Weyl particles can exist at different states in zero electromagnetic field, either as free particles, or at localized states described by a parameter with dimensions of mass. We also calculate the electromagnetic fields that should be applied in order to modify the localization of Weyl particles at a desired rate. It is shown that they are simple electric fields, which can be easily implemented experimentally. Consequently, the localization of Weyl particles in certain materials supporting these particles could also be studied experimentally, in the framework of solid-state physics or in the framework of laser physics, using ions trapped by laser beams. In addition, a particularly important remark is that the localization of the energy of the particles can lead to the generation of gravitational mass, according to Einstein's field equations of general relativity. Furthermore, in the case that the energy and localization of the particles exceeds a critical level, tiny black holes could also be created, potential candidates for the dark matter of the universe.

quant-ph↗

arXiv2022

Degenerate solutions to the massless Dirac and Weyl equations and a proposed method for controlling the quantum state of Weyl particles

In a recent work, we have shown that all solutions to the Weyl equation and a special class of solutions to the Dirac equation are degenerate in the sense that they remain unaltered under the influence of a wide variety of different electromagnetic fields. In this study, our previous work is significantly extended, providing a wide class of degenerate solutions to the Dirac equation for massless particles. The electromagnetic fields corresponding to these solutions are calculated and examples regarding both spatially constant electromagnetic fields and electromagnetic waves are also provided. Furthermore, some general solutions to the Weyl equation are presented, and the corresponding electromagnetic fields are calculated. Based on these results, a method for fully controlling the quantum state of Weyl particles using appropriate electromagnetic fields is proposed. Finally, the transition from degenerate to non-degenerate solutions as the particles acquire mass is discussed.

quant-ph↗

arXiv2022

Degenerate solutions to the Dirac equation for massive particles and their applications in quantum tunneling

In a recent work we have proven the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields, providing also some examples regarding massless particles. In the present article our results are extended significantly, providing degenerate solutions to the Dirac equation for particles with arbitrary mass, which, under certain conditions, could be interpreted as pairs of particles (or antiparticles) moving in a potential barrier with energy equal to the height of the barrier and spin opposite to each other. We calculate the electromagnetic fields corresponding to these solutions, providing also some examples regarding both spatially constant electromagnetic fields and electromagnetic waves. Further, we discuss some potential applications of our work, mainly regarding the control of the particles outside the potential barrier, without affecting their state inside the barrier. Finally, we study the effect of small perturbations to the degenerate solutions, showing that our results are still valid, in an approximate sense, provided that the amplitude of the electromagnetic fields corresponding to the exact degenerate solutions is sufficiently small.

quant-ph↗

arXiv2022

On the connection between the solutions to the Dirac and Weyl equations and the corresponding electromagnetic 4-potentials

In this paper we study in detail the connection between the solutions to the Dirac and Weyl equation and the associated electromagnetic 4-potentials. First, it is proven that all solutions to the Weyl equations are degenerate, in the sense that they correspond to an infinite number of electromagnetic 4-potentials. As far as the solutions to the Dirac equation are concerned, it is shown that they can be classified into two classes. The elements of the first class correspond to one and only one 4-potential, and are called non-degenerate Dirac solutions. On the other hand, the elements of the second class correspond to an infinite number of 4-potentials, and are called degenerate Dirac solutions. Further, it is proven that at least two of these 4-potentials are gauge-inequivalent, corresponding to different electromagnetic fields. In order to illustrate this particularly important result we have studied the denerate solutions to the force-free Dirac equation and shown that they correspond to massless particles. We have also provided explicit examples regarding solutions to the force-free Weyl equation and the Weyl equation for a constant magnetic field. In all cases we have calculated the infinite number of different electromagnetic fields corresponding to these solutions.

math-ph↗